Read Andrej Bauer on them many foundations of math, for example. Clearly he is a believer in "no one true ontology".
> Clearly he is a believer in "no one true ontology".
My point wasn't that you should aim for some kind of fictitious absence of ontological commitments, only that whatever language you use will have ontological commitments. Even the type judgement e:t has ontological implications, i.e., for the term e to be of type t presupposes that the world is such that this judgement is possible.
You can still operate under Fregean/Russellian presuppositions without sets. For example, consider the problem of bare particulars or the modeling of predicates on relations.